Alignment: Overall Summary

The instructional materials reviewed for Grade 1 did not meet the expectations for alignment to the CCSSM. The instructional materials partially meet the expectations for Gateway 1 as they appropriately focus on the major work of the grade but did not always demonstrate coherence within the grade and across other grades. The instructional materials do not meet the expectations for Gateway 2 as they did not address rigor within the grade-level standards, and there are missed opportunities in the materials when it comes to attending to the full meaning of the MPs.

The Report

Gateway One

Focus & Coherence

Partially Meets Expectations

The instructional materials reviewed for Grade 1 enVisions Math 2.0 partially meet the expectations for Gateway 1. The materials meet the expectations for focusing on the major work of the grade, but they do not meet the expectations for coherence. Some strengths were found and noted in the coherence criterion as the instructional materials partially met some of the expectations for coherence. Overall, the instructional materials allocate enough time to the major work of the grade for Grade 1, but the materials do not always meet the full depth of the standards.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 1 meet the expectations for assessing grade-level content. Overall, the instructional materials can be modified without substantially affecting the integrity of the materials so that they do not assess content from future grades within the assessments provided.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The assessment materials reviewed for Grade 1 meet expectations for focus within assessment. Content from future grades was found to be introduced; however, above grade-level assessment items, and their accompanying lessons, could be modified or omitted without significantly impacting the underlying structure of the instructional materials.

Probability, statistical distributions, and/or similarity, transformations and congruence do not appear in the Grade 1 materials.

The series is divided into topics, and each topic has a topic assessment and a topic performance assessment. Additional assessments include a placement test found in Topic 1, four cumulative/benchmark assessments, and an End-of-Year Assessment.

The topic assessments have a few items which assess future grade-level standards.

Topic 1 Assessment, problem 11 assesses a two-step problem using addition and subtraction; this is a Grade 2 standard, 2.OA.1.

Criterion 1b

The instructional materials reviewed for Grade 1 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to major clusters of the grade level standards which includes 1.OA, 1.NBT and 1.MD.A.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 1 meet the expectations for focus within major clusters. Overall, the instructional materials spend the majority of class time on the major clusters of each grade which includes 1.OA, 1.NBT and 1.MD.A.

To determine this, three perspectives were evaluated: 1) the number of topics devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days is the same as the number of lessons. A lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent, and we drew our conclusion based on that data.

Grade 1 enVision Math 2.0 includes 15 Topics with 107 lessons.

At the topic level, 11 of the 15 focus on major work. One topic of the 15 focuses on supporting work and partially supports the major work of the grade, and three of the 15 topics focus on supporting work without supporting the major work. At the topic level approximately 80 percent of the topics are focused on major work (counting the one unit which partially supports major work), and approximately 20 percent are focused on supporting work.

As mentioned above, a lesson level analysis is more representative of the instructional materials than a topic level analysis because the number of lessons within each topic is inconsistent. At the lesson level, 84 lessons focus on major work, five lessons focus on supporting work and continue to support the major work of the grade, and 16 lessons focus on the supporting work without supporting the major work. Additionally, two lessons focus on future grade level work. Approximately 15 percent of the lessons focus on supporting work, and approximately 2 percent of the lessons focus on future grade level work. At the lesson level, approximately 83 percent of the lessons focus on major work of the grade.

The following are the off-grade level lessons:

Lesson 1-9 focuses on two-step problems, a Grade 2 standard, 2.OA.1.

Lesson 3-4 focuses on elapsed time, a Grade 3 standard, 3.MD.1

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 1 do not meet the expectations for being coherent and consistent with CCSSM. The instructional materials do not have enough materials to be viable for a school year and do not always meet the depth of the standards. The majority of instructional materials do not have supporting content enhancing focus and coherence simultaneously but do have objectives which are clearly shaped by the CCSSM. Overall, the instructional materials for Grade 1 do not exhibit the characteristics of coherence.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 1 do not meet expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Supporting content is generally treated separately and does not support the major work of the grade.

The following details supporting work in the instructional materials.

Topic 6 is focused on representing and interpreting data. The majority of the work is treated separately, with many natural connections missed, and does not fully support the major work of the grade. The lessons each have questions about the graphs; however, most of the questions do not engage students with addition and subtraction.

Topic 13 is focused on time. This topic could include work on 1.NBT.1.

Topic 14 is focused on reasoning with shapes and their attributes. This topic is treated separately from major work of the grade. This topic could include work on addition and subtraction in working with groups of differing sizes and attributes.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

The amount of content designated for one grade level is not viable for one school year in order to foster coherence between grades. The pacing guide assumes one lesson per day as stated on page TP-23A. The enVision Math 2.0 Grade 1 program consists of 107 lessons, grouped in 15 topics. Assessments are not included in this count; if the 15 days of assessment are added in this would bring the count to 122 days. This is still below the standard school year of approximately 140-190 days of instruction. Significant modifications by the teacher would need to be made to the program materials to be viable for one school year and for students to master the grade-level content standards.

Indicator 1e

Materials are consistent with the progressions in the Standards
i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work
ii. Materials give all students extensive work with grade-level problems
iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials reviewed for Grade 1 partially meet the expectations for being consistent with the progressions in the Standards. Overall, the materials give students extensive work with grade-level problems and relate grade-level concepts explicitly to prior knowledge from earlier grades, but the materials do not reach the full depth of the standards and do not always clearly identify work that is off grade level.

Material related to future grade-level content is not clearly identified or related to grade-level work. The exception is the topic titled "Step up to 2nd grade" where the materials are clearly identified as Grade 2 materials. The Grade 1 materials have some instances where future grade-level content is present and not identified as such. For example:

Lesson 1-9 focuses on two-step problems, 2.OA.1.

Lesson 13-4 includes elapsed time, 3.MD.1.

There are also individual problems in some lessons which have future grade-level content. For example, Topic 15, lesson 4, problem 4 has students continuing patterns, 4.OA.5.

The content does not always meet the full depth of standards. This occurs due to a lack of lessons addressing the full depth of standards. For example:

1.OA.2 has two lessons addressing problems with three addends, lessons 5-4 and 5-5.

When looking at 1.OA.7, understanding the equal sign and determining if equations are true or false, there are two lessons, 5-3 and 5-3.

Interventions provided with lessons for students most often engage students more deeply in the work of the grade level than the lesson itself. Often, the lessons do not engage students appropriately because students are simply following directions instead of being engaged in problems. The following are some examples of lessons where the interventions would engage students more appropriately than the lesson: lessons 1-2, 2-2, 3-8, 4-2, 5-1 and 6-2.

The numbers of topics addressing Grade 1 domains are as follows: 5 out of 15 topics address Operations and Algebraic Thinking, 3 out of 15 topics address Measurement and Data, 5 out of 15 topics address Number and Operations in Base Ten, and 2 out of 15 topics address Geometry.

The materials relate grade-level concepts to prior knowledge within the introduction of each topic, for example:

"Math Background: Coherence" includes "Look Back" and "Look Ahead" commentary, connecting to mathematics that came earlier in Grade 1, explaining connections to the content within the topic, and explaining what will come later in Grade 1 and in Grade 2. An example can be found on pages 541c-541d for Topics 10 and 11.

Individual lessons also include coherence headings. An example is in lesson 10-6 on page 573A that includes the statement, "Coherence: In the previous three lessons, students used a hundred chart, a number line, place-value blocks, and pictures to add tens and ones. In this lesson, students continue to add a two-digit number and a one-digit number by drawing pictures of blocks as well as determining if they need to make a 10 when they add".

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards
i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings.
ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials reviewed for Grade 1 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, but the materials lack problems and activities that connect two or more clusters in a domain or two more domains in the grade.

The materials are designed at the cluster level, and this design feature is represented throughout the material in the form of a color-coded wheel identifying the cluster focus of each unit. The materials include learning objectives which are visibly shaped by CCSSM cluster headings, and the Topic Planner at the beginning of each topic has an example of this.

The focus of unit 1 is 1.OA.A, Solve Addition and Subtraction Problems. Lesson objectives in topic 1 include: L1 - Solve addition problems involving situations of adding one part to another part; L2 - Solve addition problems involving situations of putting two parts together; and L3 - Solve addition problems by breaking apart a total number of objects.

A similar example for Topic 12 can be found on pages 661I - 661J.

The materials for Grade 1 enVision Math2.0 do not foster coherence through grade-level connections. Most lessons in the Grade 1 program focus within a single domain and cluster. Of 107 lessons, 84 lessons focus within a single cluster and domain.

In Topic 1, lesson 1-8 is identified as addressing standards within two clusters, 1.OA.8 and 1.OA.1.

In Topic 2, three lessons (2-7, 2-8, 2-10) address standards in two or more clusters (1.OA.B, 1.OA.C, 1.OA.D), all within the same domain.

One of the 10 lessons in Topic 3 addresses more than one cluster, all within the same domain.

Although four lessons of the nine lessons in Topic 4 (4-4, 4-5, 4-6, 4-7) address more than one cluster, all clusters are within the same domain.

Although two of the seven lessons in Topic 5 (5-4, 5-5) address more than one cluster, all clusters are within the same domain.

Five of the five lessons in Topic 6, focused on supporting work of first grade, address standards within two clusters and domains, 1.MD.4, 1.OA.1, and 1.OA.2.

Topic 7 includes one lesson (7-1) that addresses more than one cluster, and the clusters are all within the same domain.

All lessons within Topic 8 are within a single cluster and domain.

Topic 9 includes one lesson that address two clusters; the remaining lessons focus on one cluster, all within the same domain.

All lessons within Topic 10 are within a single cluster and domain.

Topic 11 includes five of seven lessons that address two standards; the remaining two lessons each address one standard, all within a single cluster and domain.

All lessons within Topic 12 are within a single cluster and domain.

All lessons within Topic 13 are within a single cluster and domain.

All lessons within Topic 14 are within a single cluster and domain, with two standards being addressed within the unit.

All lessons within Topic 15 are within a single cluster and domain.

Further analysis of Topic 6, which addresses supporting work, and Topic 12, which addresses major work of measuring lengths, provided the following examples:

In Topic 6, as students represent and interpret data, they sometimes connect the use of operations to interpret data. For example, students find out how many more students like one object than another or how many students voted in all. Within the 5-lesson topic, there are 8 opportunities for students to make this connection. There are some comparison word problems (1.OA.1) within the chapter; however, opportunities to connect these problems to operations are missed. For example, on student book page 372, "Jim asks 9 members of his family for their favorite fruit. 6 people say they like oranges. The rest say they like apples. How many people say they like apples? _ people." By connecting operations to this problem, students may notice 9-6=3 or 6+3=9, and they may consider the relationship between addition and subtraction. However, these opportunities are missed.

In Topic 12, as students work with measuring lengths indirectly and by iterating units (1.MD.2), the lessons focus on the procedure of measuring. There are missed opportunities for students to make connections between the idea of "units" in place value (1.NBT) and "units" in measurement. The idea that smaller units compose larger units within the system is not explored. Other missed opportunities include the use of operations to compare the lengths of objects. Comparison word problems (1.OA.1) and comparing lengths using operations are not explored. For example, as students use pennies to measure objects, using operations to calculate how much longer or shorter one object is than another could address 1.OA and/or 1.NBT, depending on the quantity students are working with.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

The instructional materials reviewed for Grade 1 do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for spending sufficient time with engaging applications, but the materials do not meet expectations for any of the other indicators in rigor and balance. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students. The materials meet the expectations for attending to the specialized language of mathematics.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Grade 1 do not meet the expectations for rigor and practice-content connections. The instructional materials partially meet the expectations for spending sufficient time with engaging applications, but the materials do not meet expectations for any of the other indicators in rigor and balance. The instructional materials do identify the MPs and give students opportunities to construct viable arguments, but they do not always use the MPs to enrich the mathematics content and rarely have students critique the reasoning of other students. The materials do not attend to the full meaning of each MP and do not assist teachers in engaging students in constructing viable arguments and analyzing the arguments of other students. The materials meet the expectations for attending to the specialized language of mathematics.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials reviewed for Grade 1 enVision Math 2.0 do not meet the expectations for giving attention to conceptual understanding. The materials rarely develop conceptual understanding of key mathematical concepts where called for in specific content standards or cluster headings. Most all of the lessons in the materials have students filling out pages from the student book in a very procedural manner.

Rarely do the materials feature high quality conceptual problems or conceptual discussion questions. Some of the lessons start with a problem which could develop conceptual understanding; however, the lessons quickly transition to simply filling out the page from the student book.

Cluster 1.NBT.B focuses on understanding place value.

Topics 8 and 9 specifically address 1.NBT.B.

Lesson 8-1 cites 1.NBT.2b. Part of the essential understanding for the lesson is that numbers 11-19 “can be written as a number word.” On page 450, the numbers and words for 11-19 are presented, and the lesson states that “(t)hese numbers are made up of one group and 10 and some left over. One group of 10 is called 1 ten. The leftovers are called ones.” Instead of beginning work with the numbers 11-19 by developing the concept of 10 as a bundle of ten ones, the materials introduce 10 as one group of 10 without specifying that 10 is a group of ten ones, and then the ones are simply leftovers. Although this lesson is students’ first exposure to understanding that the numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones, all of the questions on the pages from the student book require students to either read or write the number word names.

Lesson 8-2 cites 1.NBT.2c. Although this standard is about understanding the numbers 10, 20, 30, 40, 50, 60, 70, 80 and 90 as referring to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones), this lesson really emphasizes counting by tens more than conceptual understanding of tens. Page 456 of the teacher’s guide states “Count by 10s” and tell students to notice that the “digit at the left increases by 1 every time you count 10 more” in order to write the number 40. The instructions for the guided practice and independent practice also state to “Count by 10s. Write the numbers.” Although the lesson begins with a hands-on activity using connecting cubes to make tens, the rest of the lesson focuses on pages from the student book and pictures of connecting cubes instead of hands-on activities.

The essential question for Lesson 8-3, “Count with Groups of Tens and Leftovers,” on page 462 is “How do you know how many tens and how many leftovers are in a number?” Throughout the lesson, students count the number of tens and “leftovers” in pictures to complete pages from the student book. Although the instructions for items 7-8 on page 463 states to “(r)emind students that in a two-digit number, the digit at the left tells how many groups of 10, and the digit at the right tells how many leftover ones,” the lack of discussion of ones in the lesson does not help build conceptual understanding of the two digits of a two-digit number.

Although Lesson 8-4 includes problems to develop student understanding of how many tens and ones are in a two-digit number, the pages from the student book primarily have students using pictures of number cubes throughout the lesson instead of hands-on activities.

Lesson 8-5 cites 2.NBT.2 but focuses more on procedures than conceptual understanding. This lesson focuses on drawing models for two-digit numbers that use lines for the tens and dots for the ones.

In Lessons 9-3 and 9-4 students compare two-digit numbers based on place value using symbols. Numbers on pages from the student book are represented with pictures of base ten blocks providing students with opportunities to understand the values and number composition. In Lesson 9-3, the teacher’s guide mentions on page 511 that students “may use real place-value blocks to help them make the physical connection between the numbers,” but students are not required to use the place-value blocks to make this connection.

Lesson 9-5 focuses more on the procedure of using a number-line model to determine which numbers are greater than or less than a given number. For example, Lesson 9-5 begins with the number 24. Students are told to find a number greater than 24 and a number less than 24. Students are told numbers to the right of a number are greater than and numbers to the left are less than instead of being allowed to build the understanding needed.

Cluster 1.NBT.C focuses on using place value understanding and properties of operations to add and subtract.

Topics 10 and 11 specifically address 1.NBT.C.

Lesson 9-2, “Make Numbers on a Hundred Chart,” also cites 1.NBT.5. In this lesson students are finding numbers that are 1 more, 1 less, 10 more, and 10 less than a given two-digit number. This lesson focuses more on the procedure of using the chart than conceptual understanding of 10 more and 10 less. Although page 504 states the “(y)ou can use place-value blocks to check how the numbers change,” the focus of the lesson is really on finding numbers to the left, top, right, and bottom of a given number on the hundred chart. When students begin the page from the student book, they are not asked to find 1 more, 1 less, 10 more, and 10 less than a number to complete items 1 and 2; they are asked to complete part of the hundred chart and are given a number in a square with blank squares to the left, top, right, and bottom.

Topic 10 focuses on using models and strategies to add tens and ones. Only one lesson, Lesson 10-7, focuses solely on addition of two two-digit numbers.

In Lesson 10-1, students add tens using models, mostly pictures of connecting cubes; however, the use of facts is stressed throughout the lesson. The first problem asks 3+5 before 30+50.

In Lesson 10-2 students mentally find 10 more than a number. Although the concept is introduced using place value blocks to build conceptual understanding of 1.NBT.5, the lesson does not require students to explain their reasoning, as required in standard 1.NBT.5, for any of the 16 problems on the pages from the student book.

In Lesson 10-3 students are adding tens and ones using a hundred chart. In Lesson 10-4 students are adding tens and ones using an open number line. Both of these lessons focus more on the procedure taught in the lessons than on the conceptual understanding of using place value to add. Using place value to add tens and ones is stressed in Lesson 10-5 as students are adding tens and ones using place-value models such as ten rods and ones cubes, but this lesson that stresses conceptual understanding based on place value occurs after the lessons focused more on following a procedure.

Lesson 10-6 introduces students to a procedure for adding a one-digit number to a two-digit number. For example, students add 25 + 8 using place value blocks. The lesson tells the students to make ten to solve, and the teacher leads the students through how many tens in 25 and how many ones, then how many ones in the 8, finally asking them to make a ten with the ones and asking how many ones are leftover. The essential question on page 574 is “How does making a ten help you add?” The sample answer is “By making a ten with one addend, I change the problem into an easier problem.” This lesson is focused on the procedure of making ten and not building conceptual understanding.

In Lesson 10-7, the sole lesson addressing addition of two two-digit numbers, the page from the student book begins with three problems written vertically that stress addition using place-value. However, the next four problems give two numbers that are labeled as “show” and “add,” and students fill in a horizontal equation losing the focus on place-value.

Topic 11 focuses on using models and strategies to subtract tens.

In Lesson 11-1 students subtract tens using models, mostly pictures of tens-rods.

In Lesson 11-2 students are subtracting tens using a hundred chart. In Lesson 11-3 students are subtracting tens using an open number line. Both of these lessons focus more on the procedure taught in the lessons than on the conceptual understanding of using place value to subtract. Most of the items on the pages from the student book do not require students to explain their answers.

In Lesson 11-4 students use addition to subtract tens. On the pages from the student book, 6 of the 10 problems set up both the addition and subtraction equations and students simply fill in a missing number in each.

Lessons 11-5 and 11-6 allow students to practice subtracting 10. Although the pages from the student book for Lesson 11-5 suggests using 10-frames if needed, these two lessons are opportunities for students to practice strategies and procedures that they were taught in other lessons.

There are some interventions that encourage the development of conceptual understanding; however, these interventions are not meant for all students- only those not meeting the standard.

For example, in Lesson 1-2 students in the intervention activity are actually connecting cubes to combine them instead of just counting cubes such as on the page from the student book from in the lesson.

In the Lesson 1-3, students completing the intervention activity are seeing the actual manipulatives as they work on addition problems, and this is much more conceptual then the lesson pages.

Indicator 2b

The materials do not give enough opportunities for students to develop fluency and procedural skill throughout the text and especially where it is specifically called for in the standards.

There are many opportunities for children to count objects within ten and 20. However, there are not many opportunities for daily counting above 20 and not to 120 which is the first grade standard. Frequent practice with rote counting is needed in order to master counting to 120 by 1's and counting to 100 by 10's and build fluency.

Standard 1.OA.6 is adding and subtracting within 20, demonstrating fluency for addition and subtraction within 10.

There are 21 lessons addressing the standard; however, all of the lessons are within Topics 2-4. The lessons fall within the first 36 lessons of the year.

When looking at fluency within 10, there only ten lessons addressing this portion of the standard. They are all within Topic 2, and only three of those lessons focus on subtraction. Lessons 2-6, 2-7, and 2-8 are the three lessons addressing subtraction within 10. Of the three subtraction lessons, two of them use addition to subtract, so the problems in the lesson all include addition and subtraction equations. For example, in Lesson 2-7, “Think Addition to Subtract,” one problem is “6+__=8. So, 8-6=___.” The materials provide few opportunities for students to add and subtract within 10 in these lessons.

Fluency Practice Activities aligned to 1.OA.6 are found at the end of Topics 2-14. These activities are all either "Point & Tally," “Show the Word,” or "Find a Match" activities. These thirteen pages are found at the end of each Topic, not within a Lesson, so teachers would have to intentionally incorporate these activities into the lessons. Also, in some of these activities more problems are devoted to addition within 10 than subtraction within 10. For example, on page 139, there are six addition problems and two subtraction problems. On page 733, students only add to complete the activity. On page 841, there are six addition problems and two subtraction problems.

Six Fluency Practice/Assessment pages from the student book aligned to K.OA.5 are included in the instructional materials. These pages from the student book can be seen on page 75P of the teacher's edition. These pages from the student book each have 19 problems. Of the 19 problems on each sheet, 15 are addition problems. Only three problems have students use a provided addition equation to fill in the answer to a subtraction problem. One problem includes both addition and subtraction.

As stated on page 75, the Game Center at PearsonRealize.com provides online mathematics games to help build fluency, but when you go to the games only one is beneficial for a student in Grade 1 to play when practicing fluency. The "Fancy Flea" game is a game that would be better used at a higher level. It requires more conceptual knowledge, and it would be difficult for most students in Grade 1 to maneuver and understand what is expected. The "Flying Cow Incident" game is good for building fluency and the concept of using a number line to add and subtract, but since it focuses on numbers within 20 it is better suited for Grade 2. The "Jungle Quest" game is actually more about focusing on patterns than it is on addition and subtraction, which is a Grade 4 standard. The game is very confusing and you have to make sure to click the learn button to understand what is expected. The "Launch the Sheep" game is confusing and above the Grade 1 level. It is actually more of a function table type problem. "Gobbling Globs" uses numbers larger than 120. It is a good game for students in Grade 2 learning to count by 100's and 10's but too advanced for Grade 1. "The Fluency Game" is a good game for building fluency at a first grade level. Although these games are listed in the Math Background pages, they are not actually mentioned in the lesson to suggest to teachers when they may be beneficial.

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The materials reviewed in Grade 1 for this indicator partially meet the expectations for being designed so that teachers and students spend sufficient time working on engaging the applications of the mathematics. In general, some lessons designed to emphasize application do not always provide opportunities for students to apply mathematical knowledge and skills in a real-world or non-routine context.

In the materials application is limited to word problems, which is appropriate for Grade 1. However, many of the problems do not require the context; the numbers can simply be pulled out of the problem and solved by using key words, a strategy included in the instructional materials.

Most topics have at least one lesson dedicated to application. However, the emphasis of these lessons is on the standards addressed in the rest of the topic and not necessarily application. Some of these lessons do not provide opportunities for students to apply mathematical knowledge and skills in a real-world or non-routine contexts. For example, Lesson 5-7 is designated as an application lesson. In this lesson students use words, numbers, and symbols correctly in order to determine the missing number or symbol in an equation, and most of the problems are equations without context.

Lessons 1-1, 1-2, 1-7, and 1-8 include addition word problems. Most of the problems provide blanks for the numbers with the addition and equal symbols provided. Students are simply filling in the blanks using the numbers from the equation for most problems.

Lesson 1-3 focuses on solving problems with both addends unknown. Although students are solving word problems, the equations are provided with blanks for the numbers. To complete most of the problems, students take the only number provided in the word problem and write it in the first blank. The focus of the problems is more on finding combinations of numbers that equal the total than solving word problems.

Lessons 1-4, 1-5, and 1-6 include subtraction word problems. All of the problems provide blanks for the numbers with the subtraction and equal symbols provided. Students are simply filling in the blanks using the numbers from the equation for most problems.

Lesson 1-9 provides six addition and subtraction word problems. These items allow students to add and subtract within 20 to solve word problems and require students to explain their answers.

Lesson 2-9 provides addition and subtraction within 10 word problems.

The title of Lesson 4-8 is “Solve Word Problems with Facts to 20;” however, the problems provided only require addition and subtraction within 14.

Lesson 3-9 provides word problems focusing on addition within 20.

Lesson 3-10 provides word problems and sample solutions. The focus of this lesson is on critiquing the sample solutions, not application of the standard.

The three independent practice problems in Lesson 4-9 require students to write number stories. Although students complete equations, the focus of the lesson is on writing number stories, not solving word problems.

Although Lesson 5-6 includes word problems, the focus of the lesson is on filling in the blanks in bar diagrams to fill in the blanks in addition and subtraction equations.

Lessons 6-1, 6-2, 6-3, and 6-4 are aligned to 1.OA.1 and 1.OA.2; however, the focus of these lessons is on representing and interpreting data, not solving word problems. For example, in Lesson 6-1 students are answering questions using tally charts; students can answer the questions by simply counting. Lesson 6-5 is the only lesson in Topic 6 that focuses on word problems with tally charts and picture graphs.

Lesson 5-4 provides word problems that call for addition of three whole numbers. However, nine of the 11 problems on the pages from the student book provide equations with the appropriate number of blanks and the addition and equal symbols.

Lesson 5-5 provides problems requiring students to add three numbers, but none of the guided practice or independent practice problems are word problems. The lesson focuses on strategies to add numbers.

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials do not meet the expectations for balance. The majority of the lessons are very procedural. However, the fluency of facts is underdeveloped, and subtraction fluency is only given three lessons in the materials. There is a lack of conceptual understanding in the materials; most of the materials labeled as conceptual understanding miss opportunities to develop understanding and instead teach a procedure. Many lessons only focus on one aspect of rigor at a time. Often when more than one aspect of rigor is the focus of a lesson, the aspects are conceptual understanding and procedural skills. For example, in Topic 4, of the nine lessons, three target conceptual understanding and procedural skills, four target conceptual understanding, and two target application. In Topic 5, of the five lessons, four target procedural skill and conceptual understanding and one targets application. There are many missed opportunities to connect the different aspects of rigor.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for Grade 1 do not meet the expectations for practice-content connections. The materials meet the expectations for attending to the specialized language of mathematics. The materials partially meet the expectations for attending to indicators 2e and 2gi, but they do not meet expectations for 2f and 2gii. Overall, in order to meet the expectations for meaningfully connecting the Standards for Mathematical Content and the MPs, the instructional materials should carefully pay attention to the full meaning of each MP, especially MP3 in regards to students critiquing the reasoning of other students and giving teachers more guidance for implementing MP3.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The materials partially meet the expectations for identifying the MPs and using them to enrich the mathematics content within the grade. Overall, the MPs are identified and used in connection to the content standards, but the materials do not always use the MPs to enrich the mathematics content. In the materials, the MPs are over-identified, and the connections between the MPs and the content standards are not clear.

According to the teacher overview, the MPs are identified as follows:

MP1: approximately 40 lessons.

MP2: approximately 65 lessons.

MP3: approximately 50 lessons.

MP4: approximately 65 lessons.

MP5: approximately 35 lessons.

MP6: approximately 35 lessons.

MP7: approximately 35 lessons.

MP8: approximately 40 lessons.

The total number of lessons identified for the 8 MPs is approximately 365, with about 110 lessons total in the materials, so this would lead to approximately 3 to 4 MPs per lesson. With this many practices identified in each lesson, there are many times when the entire meaning of the MP is not evident in the lesson, which leads to students not being able to develop a complete understanding of the MP and its connection to the grade-level content. For example, items 8-10 on page 87 in lesson 2-2 are labeled "MP4 Model with Math. Encourage students to continue drawing pictures as needed to solve doubles problems." In this example, students are not modeling with mathematics. They are writing answers to problems including 2+2, 4+4, and 0+0 in boxes. This is one example of how the MPs do not always enrich the content. In some instances, more guidance to teachers could enrich the content, and in other instances, the connection is limited or the MP may be misidentified. Additional examples include:

In Topic 10 on page 545, items 3-11 are labeled "MP4: Model with Math. Remind students to count the number of ten rods to find the total number of tens. Guide them to understand there are 10 ones in each tens rods." Students are not modeling with mathematics because they are not getting to choose how to model the situation. An addition equation is already supplied for students, and the students have to fill in the blanks of the equation.

In Topic 2 on page 81, item 10 is labeled "MP5: Use Appropriate Tools Strategically. Count on to add. Use the number line to help." In this example, students may use the number line, however, they are not selecting the tool, only deciding whether or not to use it.

Lesson 4-1, in the "Solve & Share", cites MP 5 but does not give teachers any guidance on how to help choose an appropriate tool and, instead, has teachers give students the tool to use.

The Math Practices and Problem Solving Handbook in the front of the teacher's edition is a helpful resource in understanding the MPs and knowing what to look for in student behaviors. For example, page F23A lists six indicators to assess MP3, "Listen and look for the following behaviors to monitor students' ongoing development of proficiency with MP3" A proficiency rubric is also included.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Grade 1 do not meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials do not treat each MP in a complete, accurate, and meaningful way.

The lessons give teachers some guidance on how to implement the standards. However, many of the MPs are misidentified in the materials. Also, the materials often do not attend to the full meaning of some of the MPs.

MP1: Lesson 1-6 cites MP1. Students are asked to cross out the objects in the larger group to solve comparison problems; however, there is not a rich problem attached, only a page from the student book where the objects are already printed for the student. This does not provide the opportunity to make sense of a problem or persevere in solving it. Lesson 2-2 cites MP1. Again, a rich problem is not attached. Lesson 3-8 cites MP1; the problems provided are for fluency practice and do not provide students with rich problems to solve.

MP4: Lesson 1-1 cites MP4; however, giving the students the materials to model with and then telling them how to model them is not meeting the intention of the MP. Lesson 1-3 asks students to draw spiders both inside and outside the cave to represent the whole; telling the students what to draw does not meet the intent of MP4. Lesson 2-4 cites MP4; again, students are told how to model the problem. Lesson 2-5 cites MP4, and again, students are told how to model the problem. In Lesson 8-3 on page 462, an image shows groups of ten cubes being circled with the question posed, "Why is it helpful to circle groups of 10?" The guided practice section of this lesson directs students to circle groups of 10 and write the numbers. Students are not modeling with mathematics within this task.

MP5: Lesson 1-4 cites MP5; giving students cubes to use does not meet the intent of using appropriate tools strategically. To meet the intention students should be choosing and using their own mathematical tools. Lesson 2-1 cites MP5 but gives students a number line to use. Lesson 2-7 cites MP5, yet the lesson tells the students which tools to use. Although Lesson 4-1 gives students a number line as the tool, it cites MP5.

MP7: Lesson 2-4 cites MP7, but telling the students what to write and the numbers to look for does not have them looking for structure. Lesson 3-7 cites MP7; however, the problem does not have students looking for or making use of structure. Lesson 4-3, cites MP7. Again, the students are told how to use the ten frames, so the opportunity to look for and use structure is taken away from them.

MP8: Lesson 3-6 cites MP8, but telling students how to put the counters into the ten-frames does not have students looking for repeated reasoning. Lesson 4-5 cites MP8; telling students they can use addition to help solve subtraction word problems does not have students looking for repeated reasoning.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:

0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The materials partially meet the expectation for prompting students to construct viable arguments and analyze the evidence of others. Although the materials at times prompt students to construct viable arguments, the materials miss opportunities for students to analyze the arguments of others, and the materials rarely have students do both together.

There are some questions that do ask students to explain their thinking in the materials. MP3 is identified 48 times in the student edition. In many of the places where MP3 is identified, the students are not attending to the full meaning of the MP. For example, in lesson 8-2, MP3 is cited; however, students are not asked to analyze the arguments of others. In lessons 8-6 and 9-4, MP3 is cited, but in both lessons, students are not asked to either create an argument or analyze the arguments of others. Additional examples of this can be found in the following lessons: 1-8, 2-2, 3-5, 4-9, 5-4, 6-5, 7-3, 8-6, 9-4, 10-9, 11-2, 13-4, 14-6 and 15-2.

Examples of opportunities to construct viable arguments:

Topic 1, page 51. Sophie sees 5 small pebbles by the lake. She also sees some big pebbles. She sees a total of 7 pebbles. How many big pebbles did Sophie see? Show how you know.

Topic 1, page 57. Mia needs 8 movie tickets. She has 5 movie tickets. She buys 3 more. Does she have enough tickets now? Explain how you know with pictures, numbers, or words.

Topic 3, page 185. How can thinking about 10 help you find the answer to the addition fact 9+5? Show your work and explain.

Topic 3, page 191. How can you make 10 to solve the addition fact 8+5? Show your work and explain.

Topic 5, page 299. Find the missing number in this equation. 7+_=13. Explain how you found the missing number.

Examples of opportunities to analyze the arguments of others:

Topic 1, page 58. Do you understand? Show Me!How are the two different math arguments alike and different?

Topic 3, page 168. Becca shows 6+7 with cubes and says it is not a doubles fact. Is she correct? How do you know?

Topic 3, page 209. A pet store has 9 frogs. 5 of the frogs are green and the rest are brown. Lidia adds 5+9 and says that the store has 14 brown frogs. Circle if you agree or do not agree with Lidia's thinking. Use pictures, words, or equations to explain.

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The materials do not meet the expectation for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Usually questions have one correct answer, and there is not much guidance for teachers on how to lead discussions beyond the provided questions and answer. There are many missed opportunities to guide students in analyzing the arguments of others.

In Lesson 1-3, on page 21 students are asked, "Show how you could place the 5 pencils in these two cups. Complete the equation to show your work. Then talk to a classmate. Are your equations the same?" Students are not provided with additional guidance to help students compare equations.

In Lesson 3-10, students are given the problem statement, "A pet store has 9 frogs. 5 of the frogs are green and the rest are brown. Lidia adds 5+9 and says the store has 14 brown frogs. Circle if you agree or do not agree with Lidia's thinking. Use pictures, words, or equations to explain." Teachers are provided with one question to pose that gets at the idea of what you can do to decide if you agree or disagree with someone's thinking about the way he or she solved a problem (page 210). This question is the only one in the lesson that will elicit deeper thinking about MP3, and there is limited support for teachers on engaging students in a discussion around this idea. There are several opportunities for students to agree/disagree with a given idea, but there is limited support to develop the skills to do this.

In Lesson 4-9 on page 282, teachers are given a direction, "Ask students to identify the whole and parts in each equation. What is the whole in 6-2=4. What are the parts in your equation? What is the whole in your equation in Item 6? Are the parts and the whole the same in each equation? Are the two equations in the same fact family?" Teachers are provided with single correct responses and no support or guidance for developing a discussion or constructing arguments.

In Lesson 8-2, students explain how they know that two tens is the same as twenty and use cubes to show their answer. Teachers are not provided any guidance about how to help students construct their explanations.

In Lesson 9-2 on page 504 of the Teacher's Edition, teachers are told to "(h)ave students explain how numbers change when they show 10 more." Teachers are not provided sample explanations or guidance.

In Lesson 13-3 students are asked the following questions: "How many minutes are there in an hour?" and "Why do you think a half hour is 30 minutes?" Teachers are provided with single correct responses and no support or guidance is provided.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.

The Grade 1 instructional materials meet the expectations for attending to the specialized language of mathematics. The vocabulary words are taught and worked with at the beginning of each topic and, again, at the very end of the topic. The assumption is that Grade 1 students will remember all words from the beginning of the topic and will not need them reintroduced before they are used in a lesson.

Each lesson includes a list of important vocabulary in the topic organizer which can be found at the beginning of each topic. These vocabulary words are also noted in the "Lesson Overview" at the beginning of each lesson. The identified vocabulary words appear within the blue script that teachers may use, and the words are highlighted in the student book.

Materials lack instructions that require students to use vocabulary terms and precise mathematical language as a regular part of student learning.

Each unit includes two-sided vocabulary cards in the student edition with a word on one side and definition and/or representation on the other. The teacher's edition includes vocabulary activities at the start of each topic.

Each topic opener has a vocabulary review activity, and each topic ends with a vocabulary review activity.

There is an online game for vocabulary, Save the Word.

In topic 7 on page 393, tens digit is defined as "The tens digit in 25 is 2." While this is accurate, it doesn't attend to the full meaning that the 2 is the number of tens in 25.

Gateway Three

Usability

Not Rated

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.

N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3m - 3q

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.

N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:

N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.

N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

N/A

Indicator 3q

Materials encourage students to monitor their own progress.

N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.

N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.

N/A

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.

N/A

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.

N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

N/A

Indicator 3ac

Materials can be easily customized for individual learners.
i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations.
ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

Additional Publication Details

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

Indicator Specific item that reviewers look for in materials.

Criterion Combination of all of the individual indicators for a single focus area.

Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.

Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

Focus and Coherence

Rigor and Mathematical Practices

Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.